Mestrado em Ciência de Computadores Mestrado Integrado em Engenharia de Redes e Sistemas Informáticos VC 14/15 – TP8 Segmentation Miguel Tavares Coimbra

VC 14/15 - TP8 - Segmentation Outline Thresholding Geometric structures Hough Transform Acknowledgements: Most of this course is based on the excellent courses offered by Prof. Shree Nayar at Columbia University, USA and by Prof. Srinivasa Narasimhan at CMU, USA. Please acknowledge the original source when reusing these slides for academic purposes.

VC 14/15 - TP8 - Segmentation Topic: Thresholding Thresholding Geometric structures Hough Transform

VC 14/15 - TP8 - Segmentation Boundaries of Objects Marked by many users

VC 14/15 - TP8 - Segmentation Boundaries of Objects from Edges Brightness Gradient (Edge detection) Missing edge continuity, many spurious edges

VC 14/15 - TP8 - Segmentation Boundaries of Objects from Edges Multi-scale Brightness Gradient But, low strength edges may be very important

VC 14/15 - TP8 - Segmentation Image Machine Edge Detection Human Boundary Marking

VC 14/15 - TP8 - Segmentation Boundaries in Medical Imaging Detection of cancerous regions. [Foran, Comaniciu, Meer, Goodell, 00]

VC 14/15 - TP8 - Segmentation Boundaries in Ultrasound Images Hard to detect in the presence of large amount of speckle noise

VC 14/15 - TP8 - Segmentation Sometimes hard even for humans!

VC 14/15 - TP8 - Segmentation What is ‘Segmentation’? Separation of the image in different areas. –Objects. –Areas with similar visual or semantic characteristics. Not trivial! It is the holy grail of most computer vision problems!

VC 14/15 - TP8 - Segmentation Subjectivity A ‘correct’ segmentation result is only valid for a specific context. –Subjectivity! –Hard to implement. –Hard to evaluate. Person Suitcase Face What is the correct segmentation?

VC 14/15 - TP8 - Segmentation Core Technique: Thresholding Divide the image into two areas: –1, if f(x,y)>K –0, if f(x,y)<=K Not easy to find the ideal k magic number. Core segmentation technique –Simple –Reasonably effective Adequate threshold

VC 14/15 - TP8 - Segmentation Finding the ‘magic number’ Wrong! (k = 128) Correct (k = 74)

VC 14/15 - TP8 - Segmentation Global thresholds are not always adequate...

VC 14/15 - TP8 - Segmentation Adaptive Thresholding Adapt the threshold value for each pixel. Use characteristics of nearby pixels. How? –Mean –Median –Mean + K –... Mean of 7x7 neighborhood

VC 14/15 - TP8 - Segmentation 7x7 window; K = 775x75 window; K = 10

VC 14/15 - TP8 - Segmentation Topic: Geometric structures Thresholding Geometric structures Hough Transform

VC 14/15 - TP8 - Segmentation Points What is a point? –Pixel with a significant illumination difference to its neighbors. –Group of pixels? Spatial Mask! Need to define a threshold K. 8

VC 14/15 - TP8 - Segmentation Lines Spatial filter –One per line direction –Sensitive to line width HorizontalVertical Diagonal?

VC 14/15 - TP8 - Segmentation Edges Edge: –Spatial discontinuity of pixel amplitude. –High spatial gradient First derivative (peak) Second derivative (zero crossing)

VC 14/15 - TP8 - Segmentation Popular operators Edge detection –Great utility for several problems. –Well studied problem. A variety of solutions exists.

VC 14/15 - TP8 - Segmentation

Processing Edge Images Image Edge detection and Thresholding Noisy edge image Incomplete boundaries Edge Tracking Thinning

VC 14/15 - TP8 - Segmentation Edge Tracking Methods Adjusting a priori Boundaries Given: Approximate Location of Boundary Task: Find Accurate Location of Boundary Search for STRONG EDGES along normals to approximate boundary. Fit curve (eg., polynomials) to strong edges.

VC 14/15 - TP8 - Segmentation Edge Tracking Methods Divide and Conquer Given: Boundary lies between points A and B Task: Find Boundary Connect A and B with Line Find strongest edge along line bisector Use edge point as break point Repeat

VC 14/15 - TP8 - Segmentation Fitting Lines to Edges (Least Squares) Given: Many pairs Find: Parameters Minimize: Average square distance: Using: Note:

VC 14/15 - TP8 - Segmentation Topic: Hough Transform Thresholding Geometric structures Hough Transform

VC 14/15 - TP8 - Segmentation Hough Transform Elegant method for direct object recognition Edges need not be connected Complete object need not be visible Key Idea: Edges VOTE for the possible model

VC 14/15 - TP8 - Segmentation Image and Parameter Spaces Equation of Line: Find: Consider point: Image Space Parameter Space Parameter space also called Hough Space

VC 14/15 - TP8 - Segmentation Line Detection by Hough Transform Parameter Space Algorithm: Quantize Parameter Space Create Accumulator Array Set For each image edge increment: If lies on the line: Find local maxima in

VC 14/15 - TP8 - Segmentation Better Parameterization NOTE: Large Accumulator More memory and computations Improvement: Line equation: Here Given points find (Finite Accumulator Array Size) Image Space Hough Space ? Hough Space Sinusoid

VC 14/15 - TP8 - Segmentation Image space Votes Horizontal axis is θ, vertical is rho.

VC 14/15 - TP8 - Segmentation

Mechanics of the Hough Transform Difficulties –how big should the cells be? (too big, and we merge quite different lines; too small, and noise causes lines to be missed) How many lines? –Count the peaks in the Hough array –Treat adjacent peaks as a single peak Which points belong to each line? –Search for points close to the line –Solve again for line and iterate

VC 14/15 - TP8 - Segmentation Fewer votes land in a single bin when noise increases.

VC 14/15 - TP8 - Segmentation Adding more clutter increases number of bins with false peaks.

Real World Example Original Edge Detection Found Lines Parameter Space

VC 14/15 - TP8 - Segmentation Other shapes Original Edges when using circle model

VC 14/15 - TP8 - Segmentation Resources Gonzalez & Woods – Chapter 7 N. Otsu, “A threshold selection method from gray-level histograms,” IEEE Trans. Sys., Man., Cyber., vol. 9, pp. 62–66, 1979.